Similar Figures

Front

What are similar figures?

Back

Similar figures are shapes that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

What does it mean for two figures to be proportional?

Back

Two figures are proportional when the ratios of their corresponding sides are equal.

Front

How can you determine if two triangles are similar?

Back

Two triangles are similar if they satisfy one of the following criteria: AA (Angle-Angle), SSS (Side-Side-Side), or SAS (Side-Angle-Side).

Front

If two similar figures have a scale factor of 2, what does that mean?

Back

A scale factor of 2 means that each side of the larger figure is twice the length of the corresponding side of the smaller figure.

Front

What is the formula to find the area of similar figures?

Back

The area of similar figures is proportional to the square of the scale factor. If the scale factor is k, then the ratio of the areas is k².

Front

If a triangle has sides of 3 cm, 4 cm, and 5 cm, what are the sides of a similar triangle with a scale factor of 3?

Back

The sides of the similar triangle would be 9 cm, 12 cm, and 15 cm.

Front

What is the relationship between the perimeters of similar figures?

Back

The ratio of the perimeters of similar figures is equal to the scale factor.

Front

If two similar rectangles have a scale factor of 1:4, how do their areas compare?

Back

The area of the larger rectangle is 16 times the area of the smaller rectangle, since the area ratio is the square of the scale factor (4² = 16).

Front

How do you find a missing side length in similar figures?

Back

To find a missing side length, set up a proportion using the lengths of corresponding sides from the two similar figures.

Front

If one side of a similar figure is 5 cm and the corresponding side of another figure is 15 cm, what is the scale factor?

Back

The scale factor is 3:1.